Field-induced quantum phase transition in the anisotropic Kondo necklace model (original) (raw)
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Quantum phase transitions in the Kondo-necklace model
2011
Abstract: Kondo-necklace model can describe the magnetic low-energy limit of strongly correlated heavy fermion materials. There exists multiple energy scales in this model, each of which indicates a phase. Here, we study quantum phase transitions between these different phases, and show the effect of anisotropies in terms of quantum information properties and the vanishing of energy gap.
Antiferromagnetic and spin-gap phases of the anisotropic Kondo necklace model
Physical Review B, 2006
We have studied the effect of anisotropies on the quantum phase transition of the Kondo necklace model in dimensions D=1, 2 and 3. Both the anisotropy δ of the inter-site interaction term and anisotropy ∆ of the on-site Kondo interaction have been included. We use a bond operator method with constraints implemented in mean field approximation. Starting from the paramagnetic phase we determine the critical ratio (t/J)c of the quantum critical point and associated scaling exponents of the Kondo-singlet gap. We show that in the case of easy-axis type anisotropy δ > 1 a qualitatively new behavior in comparison to the conventional Kondo necklace model with (δ,∆)=(0,1) appears. We have also obtained the antiferromagnetic order parameter in the long range ordered phase for t > tc.
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the ‘perturbative continuous unitary transformations’ approach to calculate the energy gap and spin–spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green’s function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.
Phase diagram of the one-dimensional anisotropic Kondo-necklace model
Physical Review B, 2008
The one dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction (J) between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value, Jc. Moreover, our results show that the onset of anisotropy in the XY term of the itinerant interactions develops the antiferromagnetic order for J < Jc. This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic XY interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.
Phase diagram of the Kondo necklace model at finite temperatures
Physica B: Condensed Matter, 2005
A simplified version of the Kondo lattice model, the Kondo necklace model, is studied at finite temperature using a representation for the localized and conduction electron spins in terms of local Kondo singlet and triplet operators. We calculate the double time Green's functions to get the dispersion relation of the excitations of the system. We show that in 3-d there is an antiferromagnetic ordered state at finite temperatures, but in 2-d long-range magnetic order occurs
Analysis of the Antiferromagnetic Phase Transitions of the 2D Kondo Lattice
Physical Review Letters, 2009
We have studied the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the non-linear sigma model. A renormalization group analysis of the competing Kondo -RKKY interaction was carried out to 1-loop order in the ǫ expansion, and a new quantum critical point is found, dominated by Kondo fluctuations. In addition, the spin-wave velocity scales logarithmically near the new QCP, i.e breakdown of hydrodynamic behavior. The results allow us to propose a new phase diagram near the AFM fixed point of this 2D Kondo lattice model.
Phase diagram of the Kondo necklace model with planar and local anisotropies
The European Physical Journal B, 2010
We use the density matrix renormalization group to study the quantum critical behavior of a one-dimensional Kondo necklace model with two anisotropies: η in the XY interaction of conduction spins and Δ in the local exchange between localized and conduction spins (characterized by J). To do so, we calculate the gap between the ground and the first excited state for different values of η and Δ as a function of J, and fit it to a Kosterlitz-Thouless tendency; the point in which the gap vanishes is the quantum critical point Jc. To support our results, we calculate correlation functions and structure factors near the obtained critical points. The use of entanglement measures, specifically the von Neumann block entropy, to identify the quantum phase transition is also presented. Then we build the phase diagram of the model: for every Δ considered, any value of η > 0 generates a quantum phase transition from a Kondo singlet to an antiferromagnetic state at a finite value of J, and as η diminishes, so does Jc; when Δ diminishes for a fixed η, Jc increases, favoring the antiferromagnetic state.
Itinerant antiferromagnetism in infinite dimensional Kondo lattice
Physical Review B, 2010
Highly accurate numerical results for single-particle spectrum and order parameter are obtained for the magnetically ordered Kondo lattice by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. Hybridized energy bands involving local spins are identified in the Néel state as a hallmark of itinerant antiferromagnetism. At the boundary of the reduced Brillouin zone, the twofold degeneracy remains in spite of the doubled unit cell. This degeneracy results if the molecular field felt by localized spins has identical magnitude and reversed direction with that of conduction electrons. The persistent Kondo effect is responsible for the behavior. The antiferromagnetic quantum transition occurs inside the itinerant regime, and does not accompany the itinerant-localized transition.
Field induced magnetic quantum critical behavior in the Kondo necklace model
Journal of Magnetism and Magnetic Materials, 2008
The Kondo necklace model augmented by a Zeeman term, serves as a useful model for heavy fermion compounds in an applied magnetic field. The phase diagram and thermodynamic behavior for arbitrary dimensions d has been investigated previously in the zero field case [D. Reyes, M. Continentino, Phys. Rev. B 76 (2007) 075114. ]. Here we extend the treatment to finite fields using a generalized bond operator representation for the localized and conduction electrons spins. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. Two critical magnetic fields are found namely, a critical magnetic field called henceforth h c1 and a saturation field nominated h c2 . Then three important regions can be investigated: (i) Kondo spin liquid state (KSL) at low fields hoh c1 ; (ii) destruction of KSL state at hXh c1 and appearance of a antiferromagnetic state; and (iii) saturated paramagnetic region above the upper critical field h c2 .
Thermodynamic quantum critical behavior of the Kondo necklace model
Physical Review B, 2007
We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions d using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in d ≥ 3 there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T = 0. The line of Neel transitions for d > 2 varies with the distance to the quantum critical point QCP |g| as, TN ∝ |g| ψ where the shift exponent ψ = 1/(d − 1). In the paramagnetic side of the phase diagram, the spin gap behaves as ∆ ≈ p |g| for d ≥ 3 consistent with the value z = 1 found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for kBT ≫ ∆ and along the non-Fermi liquid trajectory. For kBT ≪ ∆, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.